Rogue-wave-like characteristics in femtosecond supercontinuum generation

Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves

The Cartesian coordinate system is not sufficient to study wave propagation on the coastline or in the sea where the terrain is extremely complicated, so it is necessary to study it in an unconventional coordinate system, fractals. In this paper, from the governing equations of fluid, the fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal by using multi-scale analysis and perturbation method. Based on the equation, the rogue-wave solution is obtained by the integral preserving transformation to explain some serious threats at sea.

Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularization of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counterpropagating dispersive dam break flows, as in the box problem recently studied by El, Khamis, and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.

Search for rogue waves in Bose-Einstein condensates via a theory-guided neural network

An important and incompletely answered question is whether machine learning methods can be used to discover the excitation of rogue waves (RWs) in nonlinear systems, especially their dynamic properties and phase transitions. In this work, a theory-guided neural network (TgNN) is constructed to explore the RWs of one-dimensional Bose-Einstein condensates. We find that such method is superior to the ordinary deep neural network due to theory guidance of underlying problems. The former can directly give any excited location, timing, and structure of RWs using only a small amount of dynamic evolution data as the training data, without the tedious step-by-step iterative calculation process. In addition, based on the TgNN approach, a phase transition boundary is also discovered, which clearly distinguishes the first-order RW phase from the non-RW phase. The results not only greatly reduce computational time for exploring RWs, but also provide a promising technique for discovering phase transitions in parameterized nonlinear systems.

Dynamics of optical rogue wave generation in dispersion oscillating fibers

We present an in-depth investigation of optical rogue waves (ORWs) during picosecond supercontinuum generations in photonic crystal fibers with periodic landscapes of group velocity dispersion and nonlinearity, namely dispersion oscillating fibers (DOFs). Specifically, it is shown via ensembles of numerical simulations that during supercontinuum generations, the rogue nature of extreme and rare events formed in uniform fibers can be effectively manipulated in DOFs. This is also verified by comparing single evolution dynamics in different dispersion longitudinal profiles. For investigating the influence of slow dynamics of ORW generation in DOFs, we increase the propagating distance and find out MI gain is still the major factor that influences the generation of ORWs. In addition, analytical results associated with simulations indicate the rogue manipulations in DOFs are attributed to the adjustable modulation-instability-gain due to periodic dispersion variation along fiber length. Finally, unlike MI in uniform fiber, MI gain side lobes result from quasi-phase-matching (QPM) relation in DOFs provide additional degree of freedom to control generations of ORWs. We believe our results will provide not only a novel insight of understanding ORW dynamics in presence of dispersion modulations, but also a new way of harnessing rogue waves in oceanology.

Machine learning analysis of rogue solitons in supercontinuum generation

Supercontinuum generation is a highly nonlinear process that exhibits unstable and chaotic characteristics when developing from long pump pulses injected into the anomalous dispersion regime of an optical fiber. A particular feature associated with this regime is the long-tailed “rogue wave”-like statistics of the spectral intensity on the long-wavelength edge of the supercontinuum, linked to the generation of a small number of “rogue solitons” with extreme red-shifts. Whilst the statistical properties of rogue solitons can be conveniently measured in the spectral domain using the real-time dispersive Fourier transform technique, we cannot use this technique to determine any corresponding temporal properties since it only records the spectral intensity and one loses information about the spectral phase. And direct temporal characterization using methods such as the time-lens has resolution of typically 100’s of fs, precluding the measurement of solitons which possess typically much shorter durations. Here, we solve this problem by using machine learning. Specifically, we show how supervised learning can train a neural network to predict the peak power, duration, and temporal walk-off with respect to the pump pulse position of solitons at the edge of a supercontinuum spectrum from only the supercontinuum spectral intensity without phase information. Remarkably, the network accurately predicts soliton characteristics for a wide range of scenarios, from the onset of spectral broadening dominated by pure modulation instability to near octave-spanning supercontinuum with distinct rogue solitons.

Rogue Wave Type Solutions and Spectra of Coupled Nonlinear Schrödinger Equations

The formation of rogue oceanic waves may be the result of different causes. Various factors (winds, currents, dispersive focussing, depth, nonlinear focussing and instability) make this subject intriguing, and yet its understanding is quite relevant to practical issues. Here, we deal only with the nonlinear character of this dynamics, which has been recognised as the main ingredient to rogue wave formation. In this perspective, the formation of rogue waves requires a non-vanishing and unstable background such as a nonlinear regular wave train with attractive self-interaction. The simplest, best known model of such dynamics is the universal nonlinear Schrödinger equation. This has proven to serve as a good approximation in various contexts and over a broad range of experimental settings. This model aims to give the slow evolution of the envelope of one monochromatic wave due to nonlinearity. Here, we naturally consider the same problem for the envelopes of two weakly resonant monochromatic waves. As for the nonlinear Schrödinger equation, which is integrable, we adopt an integrable model to describe the interaction of two waves. This is the system of two coupled nonlinear Schrödinger equations (Manakov model) with self- and cross-interactions that may be both defocussing and focussing. We first discuss the linear stability properties of the background by computing the spectrum for all values of the parameters such as coupling constants and amplitudes. In particular, we relate the instability bands to properties of the spectrum and compute the gain function (or growth rate). We also relate to the stability spectrum the value of the spectral variable, which corresponds to a rogue wave solution. In contrast with the nonlinear Schrödinger equation, different types of single rogue wave exist that correspond to different values of the spectral variable even in the same spectrum. For these critical values, which are completely classified, we give the corresponding explicit expression of the rogue wave solution that follows from the well known Darboux–Dressing transformation method. Although not all systems of two coupled nonlinear Schrödinger equations that have been derived in water wave dynamics are integrable, our investigation contributes to the understanding of new effects due to wave coupling, at least for model equations that, even if not integrable, are close enough to the model considered here. For instance, our findings lead to investigate rogue waves generated by instabilities due to self- and cross-interactions of defocusing type. An illustrative selection of two coupled rogue waves solutions is displayed.

Route towards extreme optical pulsation in linear cavity ultrafast fibre lasers

Pathways towards the generation of extreme optical pulsation in a chaotic transition regime in a linear fibre laser cavity configuration are presented. In a thulium mode-locked fibre laser, extreme events that can be controllably induced by manipulating the cavity birefringence for pulse energies exceeding the single soliton pulse operating regime are studied in detail for the first time. While a solitonic pulsation structure at the fundamental repetition rate is maintained, additional energy is shed in a chaotic manner, leading to broader spectral generation and shorter pulse durations whose behaviour deviates significantly from a classical statistical distribution. These pulses display markedly different characteristics from any previously reported extreme events in fibre lasers associated with multiple solitons and pulse bunching, thus presenting a novel observation of extreme pulsation. Detailed noise studies indicate that significant enhancement of relaxation oscillations, modulation instability and the interplay with reabsorption mechanisms contribute in this transient chaotic regime. The extreme pulsation generated in a compact fibre laser without any additional nonlinear attractors can provide an attractive platform to accelerate the exploration of the underlying physics of the chaos observed in mode-locked laser systems and can lead to novel fibre laser cavity designs.

Solitons and rogue waves in spinor Bose-Einstein condensates

We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F=1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of a partially coherent wave field, i.e., a wave field characterized by a finite band spectrum with random Fourier phases. Their understanding is fundamental for the design of ships and offshore platforms. In many meteorological conditions waves in the ocean are characterized by the so-called Joint North Sea Wave Project (JONSWAP) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270 m wave tank and the other in optical fibers. In both cases, waves characterized by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results.

Freak oscillation in a dusty plasma

The freak oscillation in one-dimensional dusty plasma is studied numerically by particle-in-cell method. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in dusty plasma. Additionally, the application scope of the analytical solution of the rogue wave described by the NLSE is given.

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence.

A rogue wave is an unexpected oscillation of large amplitude and is an example of the spontaneous formation of a coherent structure out of disorder. Here, the authors develop an experimental strategy that can provide snapshots in time and thus record the real shape of optical rogue waves emerging from random noise.

Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser

We reported on the observation of dissipative rogue waves (DRWs) induced by soliton explosions in an ultrafast fiber laser. It was found that the soliton explosions could be obtained in the fiber laser at a critical pump power level. During the process of the soliton explosion, the high-amplitude waves that fulfill the rogue wave criteria could be detected. The appearance of the DRWs was identified by characterizing the intensity statistics of the time-stretched soliton profile based on the dispersive Fourier-transform method. Our findings provide the first experimental demonstration that the DRWs could be observed in the soliton explosion regime and further enhance the understanding of the physical mechanism of optical RW generation.

Breather-to-soliton transitions, nonlinear wave interactions, and modulational instability in a higher-order generalized nonlinear Schrödinger equation

We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate.

Dissipative rogue waves induced by long-range chaotic multi-pulse interactions in a fiber laser with a topological insulator-deposited microfiber photonic device

We reported on the generation of dissipative rogue waves (DRWs) induced by long-range chaotic multi-pulse interactions in a fiber laser based on a topological insulator (TI)-deposited microfiber photonic device. By virtue of the simultaneous saturable absorption effect and high nonlinearity provided by the TI-deposited microfiber, a localized, chaotic multi-pulse wave packet with strong long-range nonlinear interactions could be obtained, which gives rise to the formation of DRWs. The results might enhance the understanding of DRWs in optical systems, and further demonstrated that the TI-deposited microfiber could be considered as an excellent photonic device with both saturable absorption and highly nonlinear effects for the application field of nonlinear optics.

Effect of a weak CW trigger on optical rogue waves in the femtosecond supercontinuum generation

We numerically study the characteristics of optical rogue waves in the femtosecond supercontinuum (SC) generation and use the CW triggering mechanism to control the SC generation. Detailed simulation results show for the first time that a weak CW trigger can manipulate the behaviors of optical rogue waves in the femtosecond SC regime. For the proposed CW triggering technique which requires only wavelength tuning and is a handy approach for the active control of SC, the resultant spectrum can be greatly broadened, and the noise properties of the SC can be significantly improved in terms of both of the coherence and intensity stability.

Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers

In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications.

Suppressing Short-term Polarization Noise and Related Spectral Decoherence in All-normal Dispersion Fiber Supercontinuum Generation

The supercontinuum generated exclusively in the normal dispersion regime of a nonlinear fiber is widely believed to possess low optical noise and high spectral coherence. The recent development of flattened all-normal dispersion fibers has been motivated by this belief to construct a general-purpose broadband coherent optical source. Somewhat surprisingly, we identify a large short-term polarization noise in this type of supercontinuum generation that has been masked by the total-intensity measurement in the past, but can be easily detected by filtering the supercontinuum with a linear polarizer. Fortunately, this hidden intrinsic noise and the accompanied spectral decoherence can be effectively suppressed by using a polarization-maintaining all-normal dispersion fiber. A polarization-maintaining coherent supercontinuum laser is thus built with a broad bandwidth (780-1300 nm) and high spectral power (~1 mW/nm).

Optical rogue waves in integrable turbulence

We report optical experiments allowing us to investigate integrable turbulence in the focusing regime of the one-dimensional nonlinear Schrödinger equation (1D NLSE). In analogy with broad spectrum excitation of a one-dimensional water tank, we launch random initial waves in a single mode optical fiber. Using an original optical sampling setup, we measure precisely the probability density function of optical power of the partially coherent waves rapidly fluctuating with time. The probability density function is found to evolve from the normal law to a strong heavy-tailed distribution, thus revealing the formation of rogue waves in integrable turbulence. Numerical simulations of 1D NLSE with stochastic initial conditions quantitatively reproduce the experiments. Our numerical investigations suggest that the statistical features experimentally observed rely on the stochastic generation of coherent analytic solutions of 1D NLSE.

Optical rogue waves associated with the negative coherent coupling in an isotropic medium

Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves.

Vector rogue waves and baseband modulation instability in the defocusing regime

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.

Chirped pulse formation dynamics in ultra-long mode-locked fiber lasers

By modeling giant chirped pulse formation in ultra-long, normally dispersive, mode-locked fiber lasers, we verify convergence to a steady-state consisting of highly chirped and coherent, nanosecond-scale pulses, which is in good agreement with recent experimental results. Numerical investigation of the transient dynamics reveals the existence of dark soliton-like structures within the envelope of the initial noisy pulse structure. Quasi-stationary dark solitons can persist throughout a large part of the evolution from noise to a stable dissipative soliton solution of the mode-locked laser cavity.

Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers

We report on experimental studies of coherence and fluctuations in noise-like pulse trains generated by ultrafast fiber oscillators. By measuring the degree of first-order coherence using a Young's-type interference experiment, we prove the lack of phase coherence across the seemingly regular array of pulses. We further quantify the pulse-to-pulse fluctuations by recording the single-shot spectra of the megahertz pulse train, and experimentally demonstrate the existence of spectral fluctuations that remain unresolved in conventional time-averaged ensemble measurements. Phase incoherence and spectral fluctuations are contrasted with quantified coherence and spectral stability when the laser is soliton mode-locked.

Taming rogue waves in vector Bose-Einstein condensates

Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons.

Rogue waves emerging from the resonant interaction of three waves

We introduce a novel family of analytic solutions of the three-wave resonant interaction equations for the purpose of modeling unique events, i.e., "amplitude peaks" which are isolated in space and time. The description of these solutions is likely to be a crucial step in the understanding and forecasting of rogue waves in a variety of multicomponent wave dynamics, from oceanography to optics and from plasma physics to acoustics.

Real-time full bandwidth measurement of spectral noise in supercontinuum generation

The ability to measure real-time fluctuations of ultrashort pulses propagating in optical fiber has provided significant insights into fundamental dynamical effects such as modulation instability and the formation of frequency-shifting rogue wave solitons. We report here a detailed study of real-time fluctuations across the full bandwidth of a fiber supercontinuum which directly reveals the significant variation in measured noise statistics across the spectrum, and which allows us to study correlations between widely separated spectral components. For two different propagation distances corresponding to the onset phase of spectral broadening and the fully-developed supercontinuum, we measure real time noise across the supercontinuum bandwidth, and we quantify the supercontinuum noise using statistical higher-order moments and a frequency-dependent intensity correlation map. We identify correlated spectral regions within the supercontinuum associated with simultaneous sideband generation, as well as signatures of pump depletion and soliton-like pump dynamics. Experimental results are in excellent agreement with simulations.

Multistate intermittency and extreme pulses in a fiber laser

In our recent Letter [Phys. Rev. Lett. 107, 274101 (2011)], we demonstrated that slow random perturbations of a system parameter were responsible for the emergence of rogue waves in a fiber laser with coexisting attractors. In this paper we investigate how the probability of a particular state to appear in multistate intermittency can be controlled by low-pass noise filtering. We show that the probability of some states depends nonmonotonously on the noise amplitude and cutoff frequency. The conditions for the emergence of extreme pulses in a erbium-doped fiber laser are analyzed numerically and experimentally.

Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves

We construct and discuss a semirational, multiparametric vector solution of coupled nonlinear Schrödinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright- and dark-rogue solutions, and novel vector unusual freak waves. The vector rogue waves could be of great interest in a variety of complex systems, from optics and fluid dynamics to Bose-Einstein condensates and finance.

Controllable optical rogue waves in the femtosecond regime

We derive analytical rogue wave solutions of variable-coefficient higher-order nonlinear Schrödinger equations describing the femtosecond pulse propagation via a transformation connected with the constant-coefficient Hirota equation. Then we discuss the propagation behaviors of controllable rogue waves, including recurrence, annihilation, and sustainment in a periodic distributed fiber system and an exponential dispersion decreasing fiber. Finally, we investigate nonlinear tunneling effects for rogue waves.

Rogue-wave-like statistics in ultrafast white-light continuum generation in sapphire

We experimentally study the statistics of the white-light continuum generated by focusing of 130 fs, 800 nm pulses in a sapphire plate and show that the statistical distributions of the spectral intensity of the blue-shifted continuum components obey the extreme-value statistics. This rogue-wave-like behavior is detected only within a narrow input-pulse energy interval. By the use of numerical simulations, we show that the observed rogue-wave-like behavior is associated with pulse splitting and build-up of intense trailing pulse. The extreme events are thereafter suppressed by the intensity clamping.

Control of pulse-to-pulse fluctuations in visible supercontinuum

Long-pulse supercontinuum sources are initiated by modulation instability and consequently suffer from stochastic shot-to-shot variations of their spectral power density. In this paper, we provide a measurement of pulse-to-pulse fluctuations over the whole supercontinuum spectrum, and we show that their spectral dependence follows the group index curve of the fiber. Then, we demonstrate a significant reduction of supercontinuum pulse-to-pulse fluctuations in the visible by using a photonic crystal fiber with longitudinally tailored guidance properties. We finally show numerically that this new source would allow a significant improvement of the signal-to-noise ratio in fluorescence microscopy.

An adaptive filter for studying the life cycle of optical rogue waves

We present an adaptive numerical filter for analyzing fiber-length dependent properties of optical rogue waves, which are highly intense and extremely red-shifted solitons that arise during supercontinuum generation in photonic crystal fiber. We use this filter to study a data set of 1000 simulated supercontinuum pulses, produced from 5 ps pump pulses containing random noise. Optical rogue waves arise in different supercontinuum pulses at various positions along the fiber, and exhibit a lifecycle: their intensity peaks over a finite range of fiber length before declining slowly.

Experimental signatures of dispersive waves emitted during soliton collisions

We report experimental evidence of dispersive waves with enhanced redshift generated through soliton collisions in a photonic crystal fiber with two zero-dispersion wavelengths. Experiments are performed to study both controlled collisions under twin-pulse excitation, as well as spontaneous collisions arising from noise-induced supercontinuum generation. Experimental results for the spectral and statistical properties are in good agreement with numerical simulations and are shown to be associated with extreme-value like distributions with long tails.

Distortionless large-ratio stretcher for ultra-short pulses using photonic crystal fiber

A large-ratio stretcher for ultra-short pulses is proposed based on photonic crystal fiber (PCF). Through proper design of the PCF structure, we obtain over 300-nm wavelength range with flattened dispersion characteristics. Analysis indicates that 1-km of such fiber can broaden over 10,000 times for ultra-short pulses with <100-fs pulse-width. Distortion due to dispersion and nonlinearity is negligible.

Giant dispersive wave generation through soliton collision

We numerically study long pulse supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths, reporting a dynamical effect where soliton collisions excite dispersive waves with 1 order of magnitude greater peak power than that arising from single-soliton generation. The dispersive wave peak power exhibits extreme-value "rogue" characteristics, with the long tail of the distribution populated by collision-related events.

Extreme-value statistics in supercontinuum generation by cascaded stimulated Raman scattering

We study experimentally the statistical fluctuations observed in a supercontinuum generated in the normal dispersion regime through cascaded stimulated Raman scattering. Specifically, we show that the statistical distribution of shot-to-shot spectral variations evolves from a quasi-Gaussian in the saturated regime for Stokes orders near the pump to a long-tailed extreme-value distribution for Stokes orders at a large separation from the pump in the unsaturated regime.